You’re right about discontinuing methane extraction, but not in regards to carbon capture. Landfills, for example, produce excessive quantities of methane. Many regions have succeeded in burning the emitted methane and capturing the carbon.
Methane is 28 times more potent than carbon dioxide as a greenhouse gas. It remains in the atmosphere for a decade before breaking down into water and carbon dioxide. It’s far better to burn and capture escaping methane, even if the carbon capture isn’t perfect.